Comparing LSTM-Based Sequence-to-Sequence Forecasting Strategies for 24-Hour Solar Proton Flux Profiles Using GOES Data

TL;DR

The paper addresses forecasting the 24-hour evolution of solar proton flux after SPE onsets using LSTM-based seq2seq models. It systematically compares six forecasting strategies across 15 architectures on a curated 40-event GOES SPE dataset with 4-fold cross-validation, showing that one-shot forecasts generally outperform autoregressive ones and that proton-only inputs often beat proton+X-ray inputs on raw data, while trend smoothing helps multi-input setups. Key contributions include a rigorous architecture and strategy comparison, insights into when data preprocessing helps, and practical guidance for real-time SPE forecasting under data scarcity. The findings inform operational space weather forecasting by clarifying design choices for input features, preprocessing, and forecasting mode under limited samples.

Abstract

Solar Proton Events (SPEs) cause significant radiation hazards to satellites, astronauts, and technological systems. Accurate forecasting of their proton flux time profiles is crucial for early warnings and mitigation. This paper explores deep learning sequence-to-sequence (seq2seq) models based on Long Short-Term Memory networks to predict 24-hour proton flux profiles following SPE onsets. We used a dataset of 40 well-connected SPEs (1997-2017) observed by NOAA GOES, each associated with a >=M-class western-hemisphere solar flare and undisturbed proton flux profiles. Using 4-fold stratified cross-validation, we evaluate seq2seq model configurations (varying hidden units and embedding dimensions) under multiple forecasting scenarios: (i) proton-only input vs. combined proton+X-ray input, (ii) original flux data vs. trend-smoothed data, and (iii) autoregressive vs. one-shot forecasting. Our major results are as follows: First, one-shot forecasting consistently yields lower error than autoregressive prediction, avoiding the error accumulation seen in iterative approaches. Second, on the original data, proton-only models outperform proton+X-ray models. However, with trend-smoothed data, this gap narrows or reverses in proton+X-ray models. Third, trend-smoothing significantly enhances the performance of proton+X-ray models by mitigating fluctuations in the X-ray channel. Fourth, while models trained on trendsmoothed data perform best on average, the best-performing model was trained on original data, suggesting that architectural choices can sometimes outweigh the benefits of data preprocessing.

Figures (3)

• Figure 1: Example of well-connected SPE on 6 November 1997, from b11. (top) GOES X-ray flux and (bottom) solar proton flux data. Vertical dashed line indicates flare peak time. Horizontal dashed line indicates threshold of SPE (10 pfu).
• Figure 2: Model structures. (top) Autoregressive forecasting mode and (bottom) one-shot forecasting mode. Blue and orange boxes represent LSTM layers in the encoder and decoder, respectively. Green boxes denote fully connected layers. White boxes represent input/output arrays or intermediate variables, and purple boxes indicate attention modules.
• Figure 3: Examples of forecasting results from the best-performance model P_orig_OS, 512-8 configuration). From top to bottom: (1) S1-class SPE observed on 8 March 2011 at 01:05 UT, (2) S2-class SPE observed on 26 December 2001 at 06:05 UT, (3) S3-class SPE observed on 10 September 2017 at 16:45 UT, (4) Decreasing-phase region of the same S3-class SPE. Vertical dashed line indicates the forecasting start time. Left side of vertical line shows proton flux profiles as input, while the right side displays both the forecast and the observed values. Blue line is the input proton flux data. Orange line is the observed proton flux. Green line is the prediction result.